Brakes come on all by themselves

Our 2004 MPV Van recently began applying its own brakes. After being driven for about 5 minutes it would begin to need more and more gas pedal to maintain speed. It did not take long to realize that the car was braking since lifting the right foot caused rapid deceleration and then a complete stop. The problem can pass, or ease up, after a while, and return again, but it is not safe to drive like this and it will surely ruin the pads/rotors.
When testing the car to see if everything is moving freely before taking off I will place it in Drive and let off the brake pedal. If it moves without applying the accelerator it is not grabbing. I will even test again by moving it to Neutral and watching the speed as indicated. If there is not a drop in velocity it is still moving freely. The brakes/calipers will close with no pressure on the pedal. As an example I have tried to drive it to a mechanic and while on the freeway done the Neutral test and then resumed driving (never touching the brake pedal) and the shortly the brakes will apply themselves.

I have had the local Firest*ne shop look at it three times and Mazda dealer twice. In order the responses were:

FS) --- there is no problem.
Mazda) --- there is no problem.
Mazda) --- front caliper sticking. (Both calipers replaced)
FS) --- I don't see a problem but maybe your rear pads are sooo worn that the piston/pistons are far enough out that the cylinder lip is catching and not allowing them to retract or bad/damaged hose. (New rear calipers and pads were installed)
FS) --- It is the ABS pump. (ABS fuse pulled to remove ABS module from the equation)

Problem continues. Firestone was used for three reasons; the problem occured nearest to them, they were open and they were aware of the problem. Have not taken the next step as I don't relish the thought of spending $1,200 plus labor on another guess. The only parts not replaced seem to be the ABS pump, brake booster, the master cylinder and hoses.

The vehicle does stop in a straight line. All four calipers are engaging and not just a little bit. If you were to let off the gas at freeway speeds it would drop to 40mph almost instantly. The van will stop itself, and quite rapidly. Rotors have never been red hot but do vaporize water instantly. It is worth noting that I am deliberately not applying the brake pedal unless absolutely necessary and when it happens on the freeway I have not touched them at all.

It isn't the rotors or the parking brake. I checked that when I found out it has rotor/drum combination on the rear wheels. While investigating that was when it was noted that all four brakes are engaging at the same time.

Rotors are straight (okay circular) and within specs. There is no vibration or pulse when applying the brake.

The pedal is hard and not spongy or soft but I honestly don't know if there is any pedal movement b/c if there is I didn't see or notice it.

Any insight would be greatly appreciated.